Geodesic
Nondegeneracy in the obstacle problem with a degenerate force term
Karen Yeressian1
1Universität Zürich, Switzerland
Interfaces and free boundaries, Tome 17 (2015) no. 2, pp. 233-244

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DOI

In this paper we prove the optimal non degeneracy of the solution u of the obstacle problem △u=fχ{u>0}​ in a bounded domain D⊂Rn, where we only require f to have a nondegeneracy of the type f(x)≥λ∣(x1​,⋯,xp​)∣α for some λ>0, 1≤p≤n (an integer) and α>0. We prove optimal (2+α)-th order non degeneracy. We also prove the optimal growth with the assumption ∣f(x)∣≤Λ∣(x1​,⋯,xp​)∣α for some Λ≥0 and the porosity of the free boundary.
DOI : 10.4171/ifb/340
Classification : 35-XX
Mots-clés : Free boundary, obstacle problem, degenerate, optimal growth, optimal non degeneracy, porosity

Karen Yeressian  1

1 Universität Zürich, Switzerland 
Karen Yeressian. Nondegeneracy in the obstacle problem with a degenerate force term. Interfaces and free boundaries, Tome 17 (2015) no. 2, pp. 233-244. doi: 10.4171/ifb/340
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     title = {Nondegeneracy in the obstacle problem with a degenerate force term},
     journal = {Interfaces and free boundaries},
     pages = {233--244},
     year = {2015},
     volume = {17},
     number = {2},
     doi = {10.4171/ifb/340},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/340/}
}
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